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<p>Test math functions.  
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &quot;<a class="el" href="../../df/d55/_interpolation_8h_source.html">Math/Interpolation.h</a>&quot;</code><br />
<code>#include &quot;<a class="el" href="../../de/dda/_math_utilities_8h_source.html">Math/MathUtilities.h</a>&quot;</code><br />
<code>#include &quot;<a class="el" href="../../d9/d8e/cpp_types_8h_source.html">cppTypes.h</a>&quot;</code><br />
<code>#include &quot;gmock/gmock.h&quot;</code><br />
<code>#include &quot;gtest/gtest.h&quot;</code><br />
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<p><a href="../../dc/dc8/test__math_8cpp_source.html">Go to the source code of this file.</a></p>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Test math functions. </p>

<p>Definition in file <a class="el" href="../../dc/dc8/test__math_8cpp_source.html">test_math.cpp</a>.</p>
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<p>Definition at line <a class="el" href="../../dc/dc8/test__math_8cpp_source.html#l00013">13</a> of file <a class="el" href="../../dc/dc8/test__math_8cpp_source.html">test_math.cpp</a>.</p>

<p>References <a class="el" href="../../de/dda/_math_utilities_8h_source.html#l00023">almostEqual()</a>, and <a class="el" href="../../df/d55/_interpolation_8h_source.html#l00018">Interpolate::lerp()</a>.</p>
<div class="fragment"><div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;                              {</div><div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;double&gt;</a> y0(1, 2, 3);</div><div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;double&gt;</a> y1(6, 5, 4);</div><div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;</div><div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;double&gt;</a> yInterpRef = y0 + 0.75 * (y1 - y0);</div><div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;</div><div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;double&gt;</a> yInterp = <a class="code" href="../../d0/dff/namespace_interpolate.html#afc1377dccaf77dedbbbe66d826a3b829">Interpolate::lerp</a>(y0, y1, 0.75);</div><div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;</div><div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;  EXPECT_TRUE(<a class="code" href="../../de/dda/_math_utilities_8h.html#aa06ec79f1e3170ea41b58ffbf35b9fb6">almostEqual</a>(yInterp, yInterpRef, .001));</div><div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_a6f07728c866b15ff0676a9b2ebfd2ba6"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 1 &gt; Vec3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00026">cppTypes.h:26</a></div></div>
<div class="ttc" id="namespace_interpolate_html_afc1377dccaf77dedbbbe66d826a3b829"><div class="ttname"><a href="../../d0/dff/namespace_interpolate.html#afc1377dccaf77dedbbbe66d826a3b829">Interpolate::lerp</a></div><div class="ttdeci">y_t lerp(y_t y0, y_t yf, x_t x)</div><div class="ttdef"><b>Definition:</b> <a href="../../df/d55/_interpolation_8h_source.html#l00018">Interpolation.h:18</a></div></div>
<div class="ttc" id="_math_utilities_8h_html_aa06ec79f1e3170ea41b58ffbf35b9fb6"><div class="ttname"><a href="../../de/dda/_math_utilities_8h.html#aa06ec79f1e3170ea41b58ffbf35b9fb6">almostEqual</a></div><div class="ttdeci">bool almostEqual(const Eigen::MatrixBase&lt; T &gt; &amp;a, const Eigen::MatrixBase&lt; T &gt; &amp;b, T2 tol)</div><div class="ttdef"><b>Definition:</b> <a href="../../de/dda/_math_utilities_8h_source.html#l00023">MathUtilities.h:23</a></div></div>
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<p>Definition at line <a class="el" href="../../dc/dc8/test__math_8cpp_source.html#l00025">25</a> of file <a class="el" href="../../dc/dc8/test__math_8cpp_source.html">test_math.cpp</a>.</p>

<p>References <a class="el" href="../../de/dda/_math_utilities_8h_source.html#l00023">almostEqual()</a>, <a class="el" href="../../df/d55/_interpolation_8h_source.html#l00029">Interpolate::cubicBezier()</a>, and <a class="el" href="../../df/d55/_interpolation_8h_source.html#l00043">Interpolate::cubicBezierFirstDerivative()</a>.</p>
<div class="fragment"><div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;                                               {</div><div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;double&gt;</a> y0(1, 2, 3);</div><div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;double&gt;</a> y1(6, 5, 4);</div><div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;</div><div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;  <span class="keywordtype">double</span> dx = .00001;</div><div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;  <span class="keywordtype">double</span> x = 0.23;</div><div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;double&gt;</a> yInterpX = <a class="code" href="../../d0/dff/namespace_interpolate.html#a27f269a32607fe04fe81006adf6584aa">Interpolate::cubicBezier</a>(y0, y1, x);</div><div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;double&gt;</a> yInterpXdx = <a class="code" href="../../d0/dff/namespace_interpolate.html#a27f269a32607fe04fe81006adf6584aa">Interpolate::cubicBezier</a>(y0, y1, x + dx);</div><div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;</div><div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;double&gt;</a> dyInterpDxRef = (yInterpXdx - yInterpX) / dx;</div><div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;</div><div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;double&gt;</a> dyInterpDx = <a class="code" href="../../d0/dff/namespace_interpolate.html#a0629d179c5d037e812e93235139ca0d0">Interpolate::cubicBezierFirstDerivative</a>(y0, y1, x);</div><div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;</div><div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;  EXPECT_TRUE(<a class="code" href="../../de/dda/_math_utilities_8h.html#aa06ec79f1e3170ea41b58ffbf35b9fb6">almostEqual</a>(dyInterpDx, dyInterpDxRef, .001));</div><div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;</div><div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 3; i++) {</div><div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;    EXPECT_TRUE(yInterpX(i) &gt; y0(i) &amp;&amp; yInterpX(i) &lt; y1(i));</div><div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;  }</div><div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_a6f07728c866b15ff0676a9b2ebfd2ba6"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 1 &gt; Vec3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00026">cppTypes.h:26</a></div></div>
<div class="ttc" id="namespace_interpolate_html_a0629d179c5d037e812e93235139ca0d0"><div class="ttname"><a href="../../d0/dff/namespace_interpolate.html#a0629d179c5d037e812e93235139ca0d0">Interpolate::cubicBezierFirstDerivative</a></div><div class="ttdeci">y_t cubicBezierFirstDerivative(y_t y0, y_t yf, x_t x)</div><div class="ttdef"><b>Definition:</b> <a href="../../df/d55/_interpolation_8h_source.html#l00043">Interpolation.h:43</a></div></div>
<div class="ttc" id="namespace_interpolate_html_a27f269a32607fe04fe81006adf6584aa"><div class="ttname"><a href="../../d0/dff/namespace_interpolate.html#a27f269a32607fe04fe81006adf6584aa">Interpolate::cubicBezier</a></div><div class="ttdeci">y_t cubicBezier(y_t y0, y_t yf, x_t x)</div><div class="ttdef"><b>Definition:</b> <a href="../../df/d55/_interpolation_8h_source.html#l00029">Interpolation.h:29</a></div></div>
<div class="ttc" id="_math_utilities_8h_html_aa06ec79f1e3170ea41b58ffbf35b9fb6"><div class="ttname"><a href="../../de/dda/_math_utilities_8h.html#aa06ec79f1e3170ea41b58ffbf35b9fb6">almostEqual</a></div><div class="ttdeci">bool almostEqual(const Eigen::MatrixBase&lt; T &gt; &amp;a, const Eigen::MatrixBase&lt; T &gt; &amp;b, T2 tol)</div><div class="ttdef"><b>Definition:</b> <a href="../../de/dda/_math_utilities_8h_source.html#l00023">MathUtilities.h:23</a></div></div>
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<p>Definition at line <a class="el" href="../../dc/dc8/test__math_8cpp_source.html#l00046">46</a> of file <a class="el" href="../../dc/dc8/test__math_8cpp_source.html">test_math.cpp</a>.</p>

<p>References <a class="el" href="../../de/dda/_math_utilities_8h_source.html#l00023">almostEqual()</a>, <a class="el" href="../../df/d55/_interpolation_8h_source.html#l00043">Interpolate::cubicBezierFirstDerivative()</a>, and <a class="el" href="../../df/d55/_interpolation_8h_source.html#l00057">Interpolate::cubicBezierSecondDerivative()</a>.</p>
<div class="fragment"><div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;                                                {</div><div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;double&gt;</a> y0(1, 2, 3);</div><div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;double&gt;</a> y1(6, 5, 4);</div><div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;</div><div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;  <span class="keywordtype">double</span> dx = .00001;</div><div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;  <span class="keywordtype">double</span> x = 0.23;</div><div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;double&gt;</a> yInterpX = <a class="code" href="../../d0/dff/namespace_interpolate.html#a0629d179c5d037e812e93235139ca0d0">Interpolate::cubicBezierFirstDerivative</a>(y0, y1, x);</div><div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;double&gt;</a> yInterpXdx =</div><div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;      <a class="code" href="../../d0/dff/namespace_interpolate.html#a0629d179c5d037e812e93235139ca0d0">Interpolate::cubicBezierFirstDerivative</a>(y0, y1, x + dx);</div><div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;</div><div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;double&gt;</a> dyInterpDxRef = (yInterpXdx - yInterpX) / dx;</div><div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;</div><div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;double&gt;</a> dyInterpDx = <a class="code" href="../../d0/dff/namespace_interpolate.html#adf3e75f76efd5dd3425e02ab5ebd5fcd">Interpolate::cubicBezierSecondDerivative</a>(y0, y1, x);</div><div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;</div><div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;  EXPECT_TRUE(<a class="code" href="../../de/dda/_math_utilities_8h.html#aa06ec79f1e3170ea41b58ffbf35b9fb6">almostEqual</a>(dyInterpDx, dyInterpDxRef, .001));</div><div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;}<div class="ttc" id="cpp_types_8h_html_a6f07728c866b15ff0676a9b2ebfd2ba6"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 1 &gt; Vec3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00026">cppTypes.h:26</a></div></div>
<div class="ttc" id="namespace_interpolate_html_a0629d179c5d037e812e93235139ca0d0"><div class="ttname"><a href="../../d0/dff/namespace_interpolate.html#a0629d179c5d037e812e93235139ca0d0">Interpolate::cubicBezierFirstDerivative</a></div><div class="ttdeci">y_t cubicBezierFirstDerivative(y_t y0, y_t yf, x_t x)</div><div class="ttdef"><b>Definition:</b> <a href="../../df/d55/_interpolation_8h_source.html#l00043">Interpolation.h:43</a></div></div>
<div class="ttc" id="_math_utilities_8h_html_aa06ec79f1e3170ea41b58ffbf35b9fb6"><div class="ttname"><a href="../../de/dda/_math_utilities_8h.html#aa06ec79f1e3170ea41b58ffbf35b9fb6">almostEqual</a></div><div class="ttdeci">bool almostEqual(const Eigen::MatrixBase&lt; T &gt; &amp;a, const Eigen::MatrixBase&lt; T &gt; &amp;b, T2 tol)</div><div class="ttdef"><b>Definition:</b> <a href="../../de/dda/_math_utilities_8h_source.html#l00023">MathUtilities.h:23</a></div></div>
<div class="ttc" id="namespace_interpolate_html_adf3e75f76efd5dd3425e02ab5ebd5fcd"><div class="ttname"><a href="../../d0/dff/namespace_interpolate.html#adf3e75f76efd5dd3425e02ab5ebd5fcd">Interpolate::cubicBezierSecondDerivative</a></div><div class="ttdeci">y_t cubicBezierSecondDerivative(y_t y0, y_t yf, x_t x)</div><div class="ttdef"><b>Definition:</b> <a href="../../df/d55/_interpolation_8h_source.html#l00057">Interpolation.h:57</a></div></div>
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